A003760 Number of Hamiltonian paths in D_4 X P_n.

2, 40, 240, 1558, 8300, 43438, 212700, 1014700, 4691580, 21257258, 94520524, 414149254, 1791339472, 7664373014, 32481662616, 136520499746, 569599125312, 2361080470268, 9730117780704, 39888323454064

Offset

1,1

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Table of n, a(n) for n=1..20.

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs

F. Faase, Results from the counting program

Formula

a(1) = 2,

a(2) = 40,

a(3) = 240,

a(4) = 1558,

a(5) = 8300,

a(6) = 43438,

a(7) = 212700,

a(8) = 1014700,

a(9) = 4691580,

a(10) = 21257258,

a(11) = 94520524,

a(12) = 414149254,

a(13) = 1791339472,

a(14) = 7664373014,

a(15) = 32481662616,

a(16) = 136520499746,

a(17) = 569599125312,

a(18) = 2361080470268 and

a(n) = 11a(n-1) - 34a(n-2) - 22a(n-3) + 266a(n-4) - 270a(n-5) - 454a(n-6) + 986a(n-7) - 247a(n-8) - 887a(n-9) + 1013a(n-10) - 259a(n-11) - 353a(n-12) + 417a(n-13) - 225a(n-14) + 71a(n-15) - 13a(n-16) + a(n-17).

Crossrefs

Sequence in context: A370069 A359859 A012477 * A228240 A155977 A092698

Adjacent sequences: A003757 A003758 A003759 * A003761 A003762 A003763

Keyword

nonn

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

Status

approved